However, several main problems still need to be solved. (1) SGM is not differentiable due to its winner-take-all (WTA) by \(\operatorname{argmin} \) , making the system not being trained in an end-to-end manner. (2) Its differentiable counterpart, SGA [1]}, was proposed by changing the \(\operatorname{min} \)  to \(\operatorname{sum} \)  when aggregating the cost volume, and replacing the \(\operatorname{argmin} \)  with \(\operatorname{softargmin} \)  when predicting the disparity from the optimized cost volume, but still i) the update direction \(\mathbf {r}\)  when traversing from pixel \(\mathbf {p}\) -\(\mathbf {r}\)  to \(\mathbf {p}\)  needs to be predefined, and ii) the \(\operatorname{softargmin} \)  focusing on measuring the distance of the expectation of disparity map to the ground truth disparity, and hence cannot handle well multi-modal distributions in \(C_0\)  [2]}.
